Find a presentation for the quaternion group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.5 Exercise 1.5.3 Find a set of generators and relations for $Q_8$. Solution: Let $$X = \langle x, y…
Write out the Cayley table for Sym(3), Dih(8), and the quaternion group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.5 Exercise 1.5.2 Write out the group tables for $S_3$, $D_8$, and $Q_8$. Solution: Group table for $S_3$:…
Compute the order of each element in the quaternion group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.5 Exercise 1.5.1 Compute the order of each of the elements in $Q_8$. Solution: $x$ Reasoning Order 1 1…
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